Multiplication operators on weighted spaces in the non-locally convex framework
Let X be a completely regular Hausdorff space, E a topological vector space, V a Nachbin family of weights on X, and CV0(X,E) the weighted space of continuous E-valued functions on X. Let θ:X→C be a mapping, f∈CV0(X,E) and define Mθ(f)=θf (pointwise). In case E is a topological algebra, ψ:X→E is a m...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171297000112 |
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| Summary: | Let X be a completely regular Hausdorff space, E a topological vector space, V a
Nachbin family of weights on X, and CV0(X,E) the weighted space of continuous E-valued functions
on X. Let θ:X→C be a mapping, f∈CV0(X,E) and define Mθ(f)=θf (pointwise). In case E is
a topological algebra, ψ:X→E is a mapping then define Mψ(f)=ψf (pointwise). The main purpose
of this paper is to give necessary and sufficient conditions for Mθ and Mψ to be the multiplication
operators on CV0(X,E) where E is a general topological space (or a suitable topological algebra) which
is not necessarily locally convex. These results generalize recent work of Singh and Manhas based on the
assumption that E is locally convex. |
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| ISSN: | 0161-1712 1687-0425 |